Texture Painting: How to not have jagged edges when drawing?
Paint on an image that is twice the size you think you need, and you will get the better detail since this is about pixels, and downscale the image with an image editor to get the lower memory version. Make sure your UV mapping has allotted enough pixels for each island - unwrapping technique is critical for small details. In setting up your base image to paint to, perhaps consider checking the option '32 Bit Float' so that you have enough color depth to avoid jagged details, especially when painting bump maps.